Light source from an infinite distance is often referred as a point source 13 with negligible dimension, of which the light is diffused evenly in all directions representing by the broken lines 11 in FIG. 1. No light source is indeed infinitely small in reality. For example, the light emitting diodes and the pixels on image sensor do have actual dimension and therefore can be treated as an extended light source, such as a tiny line or surface light source. Nevertheless, assuming that the light source is a point light source can make certain optical analysis simpler. Therefore, derivations of equations for object and image distances, focal length and magnification have all been based on the assumption that the light source is theoretically a point light source.
Light diffused from an extended light source is represented by the solid lines 12 in FIG. 1. Differing from an isotropic point light source, light diffused from the center of an extended light source 14 spreads out less and therefore is with higher light intensity while the light from the side of the extended light source spreads out more and is with lower light intensity. Therefore, optical lens design based upon the aforementioned assumption of point light source and ignoring the features of an extended light source would result in undesirous effects, regardless of the materials used. For example, when such optical lens design is used for general lighting purposes, it results in different brightness between the central portion and the peripheral of a light and in turn affects the illuminating effect. Similarly, when such optical lens design is used in imaging, the lens fails to focus or collimate perfectly resulting in aberration, which is a fundamental problem of optical lens design causing unclear image. If the extended light source is relatively large, not simply aberration, there may also be distortion of image. Therefore, ordinary lens design such as spherical lens is not suitable for applying to point light source, in particular for larger line or surface light source. FIG. 2 compared the difference between the refracted light 21 of a point light source 23 and the refracted light 22 of an extended light source 24 through a plano-convex lens 25.
To minimize the aforesaid undesirous effect, aspherical lens is widely used in the industry. FIG. 3 shows the difference between the shape of a spherical lens 31 and the shape of an aspherical lens 32. The curvature of aspheric lenses surface can specifically grinded or molded to accommodate the size and dimension of a light source. Due to the uniqueness of the aspherical structure, convention tools do not have the aspheric processing ability, and they need special processing methods such as ultra-precision bonnet polishing method. Procurement and utilizing such sophisticated equipment results in high production costs and such high production costs would ultimately be shifted to the customers. Therefore, aspherical lens always maintains at a very high market price. Furthermore, not only the design is very complex and with high production costs, but also the plane precision of aspherical lens is also lower than the convention lens. Accordingly, a costs effective lens design with high precision, more particularly a lens design which meets the transmittance requirement for extended light source, is of the primary objective of the present invention.